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Root Finder finds all zeros (roots) of a polynomial of any degree with either real or complex coefficients using Bairstow's, Newton's, Halley's, Graeffe's, Laguerre's, Jenkins-Traub, Abert-Ehrlich, Durand-Kerner or Eigenvalue method.

RootFinder:
Finds all zeros (roots) of a polynomial of any degree with either real or complex coefficients using Bairstow's, Newton's, Halley's, Graeffe's, Laguerre's, Jenkins-Traub, Aberth-Ehrlich, Durand-Kerner or the Eigenvalue method. Furthermore Newton's methods is represented using 3 different approaches: The Method by Madsen, The Method by Grant-Hitchins and the probably the most famous the method by Jenkins-Traub. All 3 Newton variants existing in both a real coefficients and a complex coefficients version. Bairstow method can only handle real coefficients while Halley's, Graeffe's, Laguerre's, Aberth-Ehrlich and Durand-Kerner works on complex coefficients. Newton's method has quadratic convergence meaning that the number of significant digits double for each iterations while Halley's and Laguerre's has a cubic convergence meaning the number of significant digits tripe for each iterations.

Methods for Polynomial with Real coefficients

Methods for Polynomial with Complex coefficients

Newton by Madsen

Newton by Grant-Hitchins

Jenkins-Traub

Durand-Kerner

Eigenvalue

Bairstow

Bairstow by Bond

Newton by Madsen

Newton by Grant Hitchins

Laguerre

Halley

Jenkins-Traub

Graeffe by Malajovich

Durand-Kerner

Aberth-Ehrlich

A multiprecision version (20-200digits) is also available.
A more detail analysis of each method is found in the user guide that can be downloaded directly from the link: Root Finder User Guide.